Site trimer percolation on square lattices

Abstract

Percolation of site trimers (k-mers with k = 3) is investigated in a detailed way making use of an analyticalmodel based on renormalization techniques in this problem. Results are compared to those obtained here bymeans of extensive computer simulations. Five different deposition possibilities for site trimers are includedaccording to shape and orientation of the depositing objects. Analytical results for the percolation threshold pcare all close to 0.55, while numerical results show a slight dispersion around this value. A comparison with pcvalues previously reported for monomers and dimers establishes the tendency of pc to decrease as k increases.Critical exponent ν was also obtained both by analytical and numerical methods. Results for the latter give valuesvery close to the expected value 4/3 showing that this percolation case corresponds to the universality class ofrandom percolation.